A planetary internal gear is an example of a helical internal gear. A variety of planetary internal gears are provided as gears for an automatic transmission. However, recently, high quality has been also required of the gears as the quality of automatic transmissions has been enhanced.
A helical broach is used for machining of this helical internal gear. For example, a helical broach where, on an outer-circumferential part of a broach body formed in a shaft shape, a plurality of cutting teeth protruding on the radially outer-circumferential side of the broach body are arranged in a spiral shape which is twisted around the axis of the broach body from the tip-end side of the broach body to the rear-end side thereof has been proposed in PTL 1 mentioned below. In the helical broach, among the above-described cutting teeth, the cutting teeth on the tip-end side of the broach body are roughing teeth (circumference cutting teeth) and the cutting teeth on the rear-end side of the broach body are finishing teeth (the tooth thickness cutting teeth). In the finishing teeth, cutting edges are respectively formed at intersecting ridge parts between rake faces facing the tip-end side of the broach body and lateral surfaces facing any one side in a circumferential direction of the above-described broach body, and guiding edges are respectively formed at intersecting ridge parts between lateral surfaces on the opposite side to the cutting edges and the above-described rake faces.
A helical internal gear having a desired tooth profile is formed by machining a workpiece with the above-described helical broach. Specifically, teeth with a predetermined tooth height are formed at the workpiece by using a roughing tooth group whose height gradually increased and then the teeth are finished to a predetermined tooth thickness by using a finishing tooth group whose thickness gradually increased. When finishing the teeth in a predetermined tooth thickness, first, one lateral surface (a lateral surface on an acute angle side, for example) of the tooth profile is cut in the tooth thickness direction. Then, the other lateral surface (a lateral surface on an obtuse angle side, for example) of the tooth profile is cut in the tooth thickness direction, whereby the tooth profile is finished to desired tooth profile.